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Kink-Based Path Integral Calculations Of Atoms He-Ne, Randall W. Hall
Kink-Based Path Integral Calculations Of Atoms He-Ne, Randall W. Hall
Collected Faculty and Staff Scholarship
An adaptive, kink-based path integral formalism is used to calculate the ground state energies of the atoms He–Ne. The method uses an adaptive scheme to virtually eliminate the sign difficulties. This is done by using a Monte Carlo scheme to identify states that contribute significantly to the canonical partition function and then include them in the wavefunctions to calculate the canonical averages. The calculations use the 6-31G basis set and obtain both precision and accuracy.
An Adaptive, Kink-Based Approach To Path Integral Calculations, Randal W. Hall
An Adaptive, Kink-Based Approach To Path Integral Calculations, Randal W. Hall
Collected Faculty and Staff Scholarship
A kink-based expression for the canonical partition function is developed using Feynman’s path integral formulation of quantum mechanics and a discrete basis set. The approach is exact for a complete set of states. The method is tested on the 3×3 Hubbard model and overcomes the sign problem seen in traditional path integral studies of fermion systems. Kinks correspond to transitions between different N-electron states, much in the same manner as occurs in configuration interaction calculations in standard ab initio methods. The different N-electron states are updated, based on which states occur frequently during a Monte Carlo simulation, giving better estimates …